Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

Abstract

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.

21 pages, 9 figures

References in corpus (4)

• Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes
• Orientational order on surfaces - the coupling of topology, geometry, and dynamics
• Numerical computations of the dynamics of fluidic membranes and vesicles
• Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

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